DID YOU KNOW? DTIC has over 3.5 million final reports on DoD funded research, development, test, and evaluation activities available to our registered users. Click

HERE to register or log in.

# Accession Number:

## ADA019448

# Title:

## Location of a Point in a Planar Subdivision and Its Application.

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## ILLINOIS UNIV AT URBANA-CHAMPAIGN COORDINATED SCIENCE LAB

# Report Date:

## 1975-11-01

# Pagination or Media Count:

##
30.0

# Abstract:

## Given a subdivision of the plane induced by a planar graph with n vertices, in this paper we consider the problem of identifying which region of the subdivision contains a given test point. We present a search algorithm, called point-location algorithm, which operates on a suitably preprocessed data structure. The search runs in time at most 0log4sub 25n sq., while the preprocessing task runs in time at most 0n4log sub25n and requires 0n storage. The methods are quite general, since an arbitrary subdivision can be transformed in time at most 0n log n into one to which the preprocessing procedure is applicable. This solution of the point location problem yields interesting and efficient solutions of other geometric problems, such as spatial convex inclusion and inclusion in an arbitrary polygon. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#